Highly accurate calculation of the real and complex eigenvalues of one-dimensional anharmonic oscillators

TL;DR

This paper demonstrates that the Riccati-Padé method can accurately compute both real and complex eigenvalues of one-dimensional anharmonic oscillators, including bound states and resonances, across various models.

Contribution

It applies the Riccati-Padé method to multiple models, showing its effectiveness in calculating eigenvalues and resonances with high precision, including testing a WKB formula for resonances.

Findings

Accurate calculation of bound-state eigenvalues and resonances.

Validation of a WKB formula for resonance imaginary parts.

Versatility of the Riccati-Padé method across different spectral types.

Abstract

We draw attention on the fact that the Riccati-Pad\'e method developed some time ago enables the accurate calculation of bound-state eigenvalues as well as of resonances embedded either in the continuum or in the discrete spectrum. We apply the approach to several one-dimensional models that exhibit different kind of spectra. In particular we test a WKB formula for the imaginary part of the resonance in the discrete spectrum of a three-well potential.